06-03-2013, 02:29 PM
Transmission Lines and Waveguides
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INTRODUCTION
Given a particular conductor geometry for a transmission line or
waveguide, only certain patterns of electric and magnetic fields (modes)
can exist for propagating waves. These modes must be solutions to the
governing differential equation (wave equation) while satisfying the
appropriate boundary conditions for the fields.
General Guided Wave Solutions
We may write general solutions to the fields associated with the
waves that propagate on a guiding structure using Maxwell’s equations.
We assume the following about the guiding structure:
(1) the guiding structure is infinitely long, oriented along the zaxis,
and uniform along its length.
(2) the guiding structure is constructed from ideal materials
(conductors are PEC and insulators are lossless).
(3) fields are time-harmonic.
TEM Mode
Using the general equations for the transverse fields of guided waves
[Equation (3)], we see that the transverse fields of a TEM mode (defined
by Ez = Hz = 0) are non-zero only when kc = 0. When the cutoff
wavenumber of the TEM mode is zero, an indeterminant form of (0/0)
results for each of the transverse field equations.